1
GATE EE 2013
+1
-0.3
Which one of the following statements is NOT TRUE for a continuous time causal and stable LTI system?
A
All the poles of the system must lie on the left side of the j$$\mathrm\omega$$ axis
B
Zeros of the system can lie anywhere in the s-plane
C
All the poles must lie within $$\left|s\right|=1$$
D
All the roots of the characteristic equation must be located on the left side of the j$$\mathrm\omega$$ axis
2
GATE EE 2012
+1
-0.3
The unilateral Laplace transform of f(t) is $$\frac1{s^2\;+\;s\;+\;1}$$. The unilateral Laplace transform of tf(t) is
A
$$-\frac s{\displaystyle\left(s^2\;+\;s\;+\;1\right)^2}$$
B
$$-\frac{2s+1}{\displaystyle\left(s^2\;+\;s\;+\;1\right)^2}$$
C
$$\frac s{\displaystyle\left(s^2\;+\;s\;+\;1\right)^2}$$
D
$$\frac{2s+1}{\displaystyle\left(s^2\;+\;s\;+\;1\right)^2}$$
3
GATE EE 2002
+1
-0.3
Let Y(s) be the Laplace transformation of the function y(t), then the final value of the function is
A
$$\underset{s\rightarrow0}{L\mathrm{im}\;}Y\left(s\right)$$
B
$$\underset{s\rightarrow\infty}{L\mathrm{im}\;}Y\left(s\right)$$
C
$$\underset{s\rightarrow0}{L\mathrm{im}\;}sY\left(s\right)$$
D
$$\underset{s\rightarrow\infty}{L\mathrm{im}\;}sY\left(s\right)$$
4
GATE EE 1995
+1
-0.3
The Laplace transformation of f(t) is F(s). Given F(s)=$$\frac\omega{s^2+\omega^2}$$, the final value of f(t) is
A
infinity
B
zero
C
one
D
none of these
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